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Fairness has become one of the main issues in the theory of non-determinism and concurrency. Recently, the problem of proof rules for fair termination of programs (and some of its variants) has attracted considerable attention ([AO83], [APS82], [GFK83], [GFMR81], [LPS81], [P83]). However, though the main interest and motivation for the consideration of fair termination stems from concurrency, almost all of the recent results are formulated in terms of nondeterministic programs. The main reason for this is the elegance of formalisms for structured nondeterminism, such as Guarded Commands [DIJ76], and their convenience for syntax directed proofs. Other attempts use transition-systems as the program model, and temporal logic as the underlying reasoning formalism ([QS82], [P83]), thereby giving up the structured, syntax-directed, approach. A phenomenon inherently related to fairness is that of “unbounded nondeterminism”, whereby a program can produce an infinite set of final outcomes and yet always terminate. Such a behaviour is attributed to random assignments [AP83]. Thus, a classical example of a fairly terminating nondeterministic program is a “random (natural) number' generator”. The presence of unbounded nondeterminism forces the use of countable ordinals (higher than &ohgr;) in proofs of fair termination appealing directly to well-foundedness arguments.